Congruent Triangles Digital Activity Drag & Drop | Made By Teachers (2024)

FAQs

What makes triangles congruent answer key? ›

Two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Two triangles are congruent if they meet one of the following criteria. : All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.

Two triangles are similar if they have the same shape but not necessarily the same size. The corresponding angles are equal, and the corresponding sides are proportional. We can think of one similar triangle as an enlargement or a reduction of the other.

SAS Congruence Rule (Side – Angle – Side)

Two triangles are said to be congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle. Proof : In the given figure OA = OB and OD = OC.

You have to measure the length of both triangles separately, like AB, BC, and AC, and XY, YZ, and ZX. You also need to measure the angle between triangles XYZ and PQR. If you find AB=XY, BC=YZ, and the angles of both triangles equal to each other, then you have proven a congruent triangle with SAS.

SSS (Side-Side-Side)

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule. In the above-given figure, AB= PQ, BC = QR and AC=PR, hence Δ ABC ≅ Δ PQR.

What are the 5 ways to prove triangles congruent? There are five theorems that can be used to show that two triangles are congruent: the Side-Side-Side (SSS) theorem, the Side-Angle-Side (SAS) theorem, the Angle-Angle-Side (AAS) theorem, the Angle-Side-Angle (ASA) theorem, and the Hypotenuse-Leg (HL) theorem.

If two triangles have the same size and shape they are called congruent triangles. If we flip, turn or rotate one of two congruent triangles they are still congruent. If the sides of two triangles are the same then the triangles must have the same angles and therefore must be congruent.

Triangles that have exactly the same size and shape are called congruent triangles. The symbol for congruent is ≅. Two triangles are congruent when the three sides and the three angles of one triangle have the same measurements as three sides and three angles of another triangle.

Congruent means the same size and shape. It doesn't matter if they are mirror images of each other or turned around. If you could cut them out and put them on top of each other to show that they are the same size and shape, they are considered congruent. Rotations and flips don't matter.

Can you use aa to prove triangle congruence? ›

Angle-Side-Angle Postulate and Angle-Angle-Side Theorem

Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side in one triangle are congruent to two angles and the corresponding non-included side in another triangle, then the triangles are congruent.

In angle-angle side(AAS) if two angles and the one non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

For a set of triangles to be congruent, their respective sides and angles should be equal. In case of a triangle with all respective angles equal i.e. AAA condition, the sides of the triangles may or may not be equal.

SSS refers to the equality of three sides between triangles. AAS refers to the equality between two sides and an angle between triangles. SAS refers to the equality between two sides and an angle (between the sides) between triangles. ASA refers to the equality between two angles and one side between triangles.

There are 5 triangle congruence theorems - Side Side Side Theorem, Side Angle Side Theorem, Angle Side Angle Theorem, Angle Angle Side Theorem, and Right angle-Hypotenuse-Side or the Hypotenuse Leg theorem.

The ASA Theorem (angle-side-angle) says that if two angles and the side between them of one triangle are congruent to two angles and the side between of another triangle, then the triangles are congruent. There is no need to check the value of the third angle or the other two sides.